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Abstract
Metasurface-based beam splitters with high efficiency, large split angle, wide bandwidth and easy fabrication are highly desirable and still in pursuit. In this paper, we propose a heuristic scheme for designing an ultra-broadband high-efficiency power beam splitter based on a homogeneous metasurface. The conversion efficiency and total transmission intensity of the power splitter stays higher than 95% and 0.66 within the wavelength region from 604 nm to 738 nm, respectively. Particularly, the conversion efficiency can maintain greater than 99% in 58 nm bandwidth. The angle between two split beams can reach a maximum of 157.82° at the wavelength of 738 nm. In addition to simplified design and easy fabrication, the proposed power beam splitter possesses high robustness as well. We expect that our design can pave a new way for realizing high-performance metasurface-based beam splitters.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Beam splitters are optical components used to divide incident light into two parts that propagate in different directions. They can separate the polarization state, wavelength, or power of the incident light, and can be classified into three categories according to these three different working forms. The first is the polarization beam splitter [1–4], which enables to divide the incident light into two separate parts with orthogonal polarizations based on the difference in the polarization state of the light. The wavelength beam splitter [5–7] is the second one, it is used to separate light of different wavelengths. The power beam splitter [8–10] is the last one, which can split the incident light into two parts according to a specific power ratio. Equal-power beam splitter is the most common one. These beam splitters play vital roles in a variety of optical and photonic applications, such as photo cameras, interferometers, laser systems, and so on. Therefore, the beam splitters have always been one of the hot topics in research. The previously reported beam splitters are mainly implemented based on the following structures, such as photonic crystals [1], gratings [2,7], directional couplers [3,9], multimode interference (MMI) structures [4], waveguides [5], and so on. However, the conventional beam splitters are bulky and heavy, so it is difficult to integrate them into miniature photonic circuits. Therefore, the beam splitters with small volume and high efficiency are always pursued.
Metasurface, an ultra-thin artificial material, exhibits superior properties to manipulate the phase [11–14], amplitude [15–17], and polarization [18,19] of the electromagnetic waves in desired manners. In addition to possessing some special electromagnetic properties that are not available in natural materials, the metasurfaces feature smaller size and higher flexibility. Due to these advantages, the metasurfaces have been adopted to design beam splitters in recent years. In the previous literature, there have been many reports of polarization beam splitters [4,20–23] and wavelength splitters [24–27] based on metasurfaces at visible wavelengths. However, there are only few studies on the power splitter [28–30] in the visible spectrum due to difficult design. D. Zhang [28] proposed an equal-power beam splitter by adopting a metasurface composed of two arrays with opposite phase gradients. A. Ozer [29] and X. Zhang [30] respectively proposed power beam splitters operating in transmission and reflection modes based on the metasurfaces composed of a periodic array of binary cells with π phase difference between adjacent ones. Both of the above designs suffer from the challenges of complex design process, narrow bandwidth. Therefore, new schemes for metasurface-based power beam splitters with large operational bandwidth, high conversion efficiency, high transmission intensity and large split angle are highly desirable.
In this paper, we propose an equal-power beam splitter with high efficiency and large splitting angle in 134 nm bandwidth based on an all-dielectric metasurface. The supercell of the metasurface consists of only one silicon nanoblock resting on the silica substrate. The conversion efficiency and total transmission stays higher than 95% and 0.66 within the wavelength region from 604 nm to 738 nm, respectively.
2. Design
The schematic of the proposed power beam splitter is shown in Fig. 1(a), which is based on a homogeneous metasurface composed of a square array of nanoblocks. Compared to previous reports [28–31], our design simplifies the design process and experimental fabrication. In addition, fewer variable geometric parameters of this structure make the optimization of performance more convenient. The three-dimensional structure diagram of a supercell is depicted in Fig. 1(b). It is composed of a single silicon nanoblock placed on the silica substrate. The periods of the supercell along the x and y-directions are set ${P_x} = 750nm$and ${P_y} = 150nm$. For the silicon antenna, it can be viewed as a Fabry–Pérot resonator and can introduce a phase shift of approximately π at the interface. The length l and the width w is 490 nm and 100 nm, respectively, the height h is fixed to 160 nm. The aspect ratio of 1.6 significantly reduces the difficulty of experimental fabrication. We adopt Lumerical finite-difference time-domain (FDTD) Solutions package to investigate the optical properties of this design. In the simulations, periodic boundary conditions are used in both x- and y-directions and perfectly matched layer is applied along the z-direction. The optical constants of silicon are taken from Ref. [32] and the refractive index of silica is 1.45. The thickness of the silica substrate is 3µm. An x-polarized plane wave with wavelength region from 500 nm to 750 nm is normally incident from the bottom of the silica substrate.
Fig. 1. (a) Schematic of a homogeneous metasurface that acts as a beam splitter. (b) The three-dimensional structure diagram of a supercell of the metasurface.
3. Results
3.1. Optical performance of the power beam splitter
Large operational bandwidth, high conversion efficiency, high transmission and large split angle are major desired performances of a power beam splitter. The working mechanism diagram of the proposed beam splitter is shown in Fig. 2(a). The x-polarized incident light is divided into three parts that propagate along angles of θL (left side of the normal), 0 (normal direction), θR (right side of the normal). Here, the left (right) side corresponds to the negative (positive) direction of the x-axis. In this figure, the outgoing beam propagating in the normal direction is not displayed because it is almost completely suppressed by the proposed beam splitter. The intensity of the three emergent beams within the wavelength range from 600 nm to 750 nm depicted in Fig. 2(b). It can be seen that IR and IL are always the same at any wavelength. The intensity of the light propagating along the normal direction keeps lower than 0.05 in the nearly 140 nm bandwidth. Figure 2(c) shows the total transmission and conversion efficiency in the wavelength range from 600 nm to 750 nm. The red dashed line represents the total transmission of 0.66. Total transmission keeps higher than 0.66 within the wavelength region from 604 nm to 740 nm. The conversion efficiency, defined as$\eta \textrm{ = }\textrm{(}{{I}_L}\textrm{ + }{{I}_R}\textrm{)}{/I}\ast {100\%}$, remains greater than 95% in the wavelength range from 600 nm to 738 nm. Surprisingly, it can maintain above 99% in the 58 nm bandwidth, which far exceeds the performance of the previously reported metasurface-based beam splitters. By synthesizing these two optical parameters, it can be obtained that the transmission and conversion efficiency of the proposed beam splitter keep higher than 0.66 and 95% within the wavelength region from 604 nm to 738 nm (the wave band corresponding to the gray area). The normalized far-field intensity distributions of this device at some specific wavelengths are depicted in Fig. 2(d). Here, θL and θR have the same absolute value so that we only illustrate θR in detail. With the redshift of the wavelength, θR gradually increases and the corresponding split angle becomes wider. The split angle spans from 107.28° to 157.82° in the wavelength region from 604 nm to 738 nm.
Fig. 2. (a) Working mechanism of the proposed beam splitter device. An x-polarized incident light beam is divided into three parts that propagate along angles of θL (left side of the normal), 0 (normal direction), θR (right side of the normal). (b) Intensity of the three emergent beams within the wavelength region from 600 nm to 750 nm. (c) Total transmission and conversion efficiency of the beam splitter. The red dashed line represents the total transmission of 0.66, the thick and thin blue dashed lines indicate that the conversion efficiency is 95% and 99%, respectively. (d) Far-field pattern of the device at some specific wavelengths.
To understand the intrinsic mechanism of the metasurface to achieve beam splitting, as depicted in Figs. 3(a) and 3(b), we divide the antenna constituting the metasurface into two identical right-angle trapezoidal ones with opposite spatial arrangements. The lengths of the two bases of the trapezoid are ${w_1} = 30nm$, ${w_2} = 70nm$, respectively. The other geometric parameters, l and h, keep unchanged. Here, we only research the optical performance of the metasurface composed of the antenna A array. As previously reported [33–34], this type of metasurface can realize a full 2π phase shift and provide a linear phase gradient when y-polarized light is incident due to the continuous change of the length of the antenna in the y-direction. However, this phenomenon is difficult to achieve for the x-polarized light because Ex is insensitive to length changes in the y-direction. We numerically simulate the optical response of this metasurface when the x-polarized plane wave with the wavelength region of 580 nm to 740 nm is normally incident. It is noted that the period of the metasurface along y-direction is ${P_y}/2 = 75nm$. Figure 3(c) shows that the phase response (inset) and far-field profile at the wavelength of 660 nm. The phase response is obtained by extracting the phase received coordinates in the far field and setting the minimum phase to 0. For the phase response, we obtain the phase as a function of the x-coordinate by setting the monitor to be far away from the metasurface structure 1980nm (3λ) in the simulation. And then we set the phase value at the starting position of the supercell ($x ={-} 375nm$) to 0.The phase shift induced by the trapezoidal antenna varies slightly along the interface, which is around π. Therefore, a phase profile of 0-π-0 (2π) is approximately formed over a period of the metasurface, which causes the outgoing light propagates along the left and right of the normal but the intensity of these two beams is different. As depicted in Fig. 3(d), the total transmission keeps higher than 0.7 within the wavelength region from 580 nm to 740 nm, and the conversion efficiency maintains higher than 95% within the wavelength range from 576 nm to 734 nm, which means that this metasurface has relatively complete suppression of the transmitted light along the normal direction.
Fig. 3. (a) and (b) The antenna constituting the proposed metasurface is divided into two identical right-angle trapezoidal ones with opposite spatial arrangements. (c) The phase response (illustration) and far-field profile of the metasurface composed of antenna A array at the wavelength of 660 nm. (d) Total transmission and conversion efficiency of the metasurface composed of antenna A array within the wavelength region from 570 nm to 740 nm.
Finally, as the inset of Fig. 4(a), we add an array of antenna B into this metasurface to compensate the difference of intensity between the left and right directions and realize the equal-power beam splitting. The influence of the distance d between the antennas A and B in y- direction on the optical responses of the metasurface is numerically investigated. Figures 4(a) and 4(b) depict the conversion efficiency and total transmission of the metasurfaces with difference distance d. It can be seen that the conversion efficiency of these metasurfaces is almost the same and keeps above 90% within the wavelength region from 600 nm to 740 nm. Thus, these metasurfaces can act as high-efficiency power beam splitters, and our design is the simplest structure among them.
Fig. 4. (a) Conversion efficiency and (b) total transmission of the metasurface with different d (the distance between the antennas A and B in the y-direction). The metasurface is composed of the antenna A array and the antenna B array.
3.2. Influence of geometric parameters on optical performance
Considering the practical application, the beam splitter with high robustness requires low accuracy, so it is easier to be prepared by experiment. Here, the effects of three geometric parameters on the optical properties are simulated to research the robustness of the proposed beam splitter. Figure 5 depicts the performances of metasurface with different antenna width w. The other two geometric parameters l and h of the antenna remain unchanged. Figure 5(a) shows the conversion efficiency of these metasurfaces within the wavelength region from 550 nm to 750 nm. The gray dashed line indicates the conversion efficiency of 94%. It can be seen that with the increase of w, the starting wavelength of the band capable of achieving a conversion efficiency higher than 94% will be redshifted, while the ending wavelength shows a trend of redshift first and then stables at 738 nm. Figure 5(b) depicts the total transmission of these metasurfaces within the wavelength region from 550 nm to 750 nm. The gray dashed line indicates that the transmission intensity is 0.65. We define that when the conversion efficiency is higher than 94% and the transmission intensity is greater than 0.65, the metasurface exhibits efficient beam splitting, and the corresponding wavelength is viewed as the operating wavelength. Figure 5(c) shows that the bandwidth of these metasurfaces acting as efficient beam splitters and the maximum transmission intensity Imax in the operating band. The bandwidth is always larger than 100 nm when the width of the antenna varies from 70 nm to 130 nm. As w increases, Imax decreases while always stays above 0.70. Figure 5(d) illustrates the variation range of θR of these metasurfaces with different w in their respective working bands. Large split angle can always be achieved by these metasurface-based beam splitter.
Fig. 5. The simulated optical performances for metasurface with different antenna width w. (a) Conversion efficiency of these metasurfaces within the wavelength region from 550 nm to 750 nm. The gray dashed line represents the conversion efficiency of 94%. (b) Total transmission of these metasurfaces within the wavelength region from 550 nm to 750 nm. The gray dashed line represents total transmission of 0.65. (c) The bandwidth of these metasurfaces operating as efficient beam splitters, and the maximum transmission intensity Imax in the operating band. Wave band with conversion efficiency higher than 94% and transmission intensity greater than 0.65 is defined as operating band. (d) θR of these metasurfaces with different w within the corresponding bands.
Figure 6 depicts the performances of metasurface with different antenna length l. The conversion efficiency and total transmission of these metasurfaces within the wavelength region from 570 nm to 750 nm are shown in Figs. 6(a) and 6(b), respectively. When l increases from 450 nm to 510 nm, the start wavelength of the band that can achieve conversion efficiency higher than 94% is red-shifted from 576 nm to 634 nm. Since the conversion efficiency of the metasurface with length of 440 nm has a trough around wavelength 580 nm, the wave band starts from a wavelength of 604 nm, which is different from the above trend. For the ending wavelength, as l increases, it roughly shows a red-shifted trend and reaches a maximum of 740 nm at the length l of 510 nm. Figure 6(c) depicts the operating bandwidth and the maximum transmission intensity Imax in the band. The bandwidth is always larger than 100 nm when the length of the antenna varies from 440 nm to 510 nm, and it reaches a maximum of 148 nm at the length of 450 nm. For Imax, it is less affected by the length l and always maintains above 0.78. The variation range of θR of these metasurfaces with different l in their respective working bands is shown in Fig. 6(d). The maximum split angle even reaches 161.26°when the length l is 510 nm.
Fig. 6. The simulated optical performances for metasurface with different length l. (a) Conversion efficiency and (b) total transmission of these metasurfaces within the wavelength region from 570 nm to 750 nm. (c) The bandwidth of these metasurfaces acting as efficient beam splitters, and the maximum transmission intensity Imax within the band. (d) θR of the metasurfaces with different l within the corresponding bands.
The performances of metasurface with different antenna thickness h are depicted in Fig. 7. As illustrated in Fig. 7(a), the effect of h on the starting and ending wavelengths of the band capable of achieving a conversion efficiency higher than 94% is approximately the same as that of the width on them. Figure 7(b) depicts total transmission of these metasurfaces. When height h increases from 160 nm to 190 nm, the start wavelength of the band that can achieve transmission higher than 0.65 is red-shifted from 604 nm to 626 nm. For the metasurfaces with height of 140 nm and 150 nm, the wave bands of transmission greater than 0.65 begin from 635 nm. Figures 7(c) and 7(d) indicate the operating bandwidth and the variation range of θR of these metasurfaces with different h. The bandwidth can only maintain larger than 100 nm within the thickness h range from 160 nm to 180 nm. Thus, among the geometrical parameters of the metasurface, the thickness has the greatest influence on the optical performance, while the length has the least one.
Fig. 7. The simulated optical performances for metasurface with different height h. (a) Conversion efficiency and (b) total transmission of these metasurfaces within the wavelength region from 580 nm to 750 nm. (c) The bandwidth of these metasurfaces acting as efficient beam splitters, and the maximum transmission intensity Imax in the band. (d) θR of the metasurfaces with different h within the corresponding bands.
4. Discussions
4.1. Optical performance of the device under oblique incidence
All above analyses focus on the x-polarized normal incidence, in this case, the outgoing beams on the left and right sides are symmetric about the normal in the x-z plane. However, this symmetry will be broken when light is incident obliquely. Here, in order to explore more functions of the proposed device, we investigate its optical performances under oblique incidence. As shown in Fig. 8, the plane wave is incident obliquely from air into the silica substrate. In this case, refraction occurs. We define the incident angle as θi and the refraction angle as θsilica, according to Snell's law, they satisfy the formula
where nair and nsilica is respectively the refractive index of air and silica. Then, the plane wave transmits from the silica substrate to the transmission medium (air), and its interaction with the metasurface on the interface causes abnormal refraction. The anomalous refracted angle θt can be determined by the generalized Snell’s law [11],The deflection angle of the refracted light relative to the normal is exactly equal to the abnormal refraction angle. Therefore, according to Eq. (4), θL ($d\varphi ={-} 2\pi$) and θR ($d\varphi = 2\pi$) can be calculated as follows,
According to the Eqs. (5) and (6), the left directed beam will not exist in the case, $\sin {\theta _i} - {\lambda _0}/p < - 1$; while the right directed beam will disappear in the case, $\sin {\theta _i} + {\lambda _0}/p > 1$. Therefore, our design may be used as a beam deflector under oblique incidence as shown in Fig. 8. To demonstrate it, we simulate the optical performances of the device under different incident angles.The total transmission and diffraction efficiency of the proposed device for the incidence angles of 5°, 10°, 15°, 20° are depicted in Fig. 9. According to the Eq. (6), for the incidence angles of 5°, 10°, 15°, 20°, the right directed beam disappears when the wavelength is greater than 684.63 nm, 619.76 nm, 555.89 nm, 493.48 nm, respectively. In this case, the outgoing beam consists only of the left-direction beam and the one propagating along the incident angle. The diffraction efficiency, a key performance of beam deflector, is defined as the intensity of the left beam normalized to total transmission. The device is viewed as an efficient beam deflector when the diffraction efficiency is higher than 90% and the transmission is greater than 0.55. The corresponding wave band is defined as the operating band (gray area). Figure 9(a) shows that the optical properties at an oblique incidence angle of 5°, the operating band spans from 728 nm to 756 nm. According to Eq. (6), the corresponding deflected angle changes from -62.07° to -67.05°. The optical performance at an oblique incidence angle of 10° is depicted in Fig. 9(b), the operating band spans from 705 nm to 735 nm, where the deflected angle varies from -50.03° to -53.74°. At the wavelength of 730 nm, the diffraction efficiency reaches a maximum of 98%, and the total transmission is 0.74. As the angle increases, the operating band becomes narrower. Figures 9(c) and 9(d) show that when the incidence angle is 15° and 20°, the bandwidth of the device as an efficient deflector is respectively 20 nm and 10 nm.
Fig. 9. Total transmission and diffraction efficiency of the proposed device for the incidence angles of (a) 5°, (b) 10°, (c) 15°, (d) 20°. The diffraction efficiency is defined as the intensity of the left beam normalized to total transmission. The gray represents the band where the total transmission and diffraction efficiency respectively remain above 0.55 and 90%.
4.2. Optical performance of the device under y-polarized normal incidence
To explore the polarization dependency of the proposed device, we investigate its optical performance under y-polarized normal incidence. Figure 10 depicts the conversion efficiency of the proposed device under y-polarized normal incidence within the wavelength region from 600 nm to 750 nm. It can be seen that, only in the wavelength region from 608 nm to 612 nm, the conversion efficiency is higher than 90%. Moreover, the conversion efficiency almost keeps below 40% within the wavelength region from 630 nm to 738 nm. However, as mentioned above, under x-polarized normal incidence, the conversion efficiency of the design maintains higher than 94% within the wavelength from 604 nm to 738 nm. Therefore, the optical performance of this device is strongly dependent on polarization. This phenomenon can be understood from the viewpoint of directional scattering of a single antenna [35,36]. Under normal incidence, for the electric field parallel to the nanorod axis, the finite semiconductor (n = 3.5) nanorod will cause light to scatter along the left and right sides of the rod; for the magnetic field parallel to the nanorod axis, this directional scattering becomes extremely weak.
Fig. 10. Conversion efficiency of the proposed device under y-polarized normal incidence within the wavelength region from 600 nm to 750 nm.
5. Conclusions
In summary, we present a novel metasurface design for broadband, large-angle, equal-power beam splitter in the visible region. Under the x-polarized normal incidence, the conversion efficiency and total transmission intensity maintains higher than 95% and 0.66 in the 134 nm bandwidth, respectively. The split angle spans from 107.28° to 157.82° in the operating band. We also demonstrate the tolerances of the design. The results show that our design exhibits high tolerance to the width and length of the antenna. Moreover, our design can act as an efficient beam deflector under x-polarized oblique incidence. We expect that the proposed metasurface can be used as a high-performance beam splitter or deflector in compact integrated devices.
Funding
Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing, Guilin University of Electronic Technology; Fundamental Research Funds for the Central Universities; Beijing University of Posts and Telecommunications (Excellent Ph.D. Students Foundation (CX2020316)); Fund of State Key Laboratory of IPOC (BUPT) (IPOC2019ZZ03); National Natural Science Foundation of China (61671090, 61875021); National Key Research and Development Program of China (2016YFA0301300).
Disclosures
The authors declare no conflicts of interest.
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